A recuperative heat exchanger (36) is provided for use in a fuel processor (20), the heat exchanger (36) transferring heat from a fluid flow (34) at one stage of a fuel processing operation to the fluid flow (32) at another stage of the fuel processing operation. The heat exchanger (36) includes a housing (56) defining first and second axially extending, concentric annular passages in heat transfer relation to each other; a first convoluted fin (70) located in the first passage to direct the fluid flow therethrough; and a second convoluted fin (72) located in the second passage to direct the fluid flow therethrough.